14 hands is the official breakover between pony and horse.
Here's a little hint when looking at horses. Everybody thinks their horse is 15.2, when in fact, most traditional QH's are just under 15. Bay looks huge next to them, and he's a ~measured~ 15.2.
As for 'too old' - it really depends on the past use, and care the horse has gotten, and the luck of good or bad genes. I'd hope you would get someone that has 'been there done that' but still has a lot of years left, first for you, then perhaps getting handed down to the girls. I'd start looking in the teens, but don't overlook a nice sound 20 year old like that one, if she is. All that said, we were looking for a horse in the teens for ecurbh, and ended up with a 7 year old.
All horses and ponies look taller than they really are when you're standing next to them. My mare is exactly 16 hh . . . I have to stand uphill to mount from the ground if I don't want to lower my stirrup. That, or lead her into a ditch (there's never a bucket or a stump around when you need one).
Oh, if I was in the market now I'd definitely want to check out the mare I posted.
~sigh~ One day.
I remember you were a bit concerned about Cyn's youth, but she did turn out to be quite trustworthy, didn't she?
You got that right. The same applies for 'too young'. I think I read somewhere that a horse could be considered a "seasoned" horse at about 250 hours. You could have a 20yr old that hasn't seen 250 hours in it's whole life, and a 4yr old that's already seen 500. It's all relative. Experience is the key. Horses should come with an Hour Meter, like a tractor! ;o)